Potassium intercalates between graphite layers and donates electron density to the graphitic pi system. Occupation of formerly less populated electronic states raises the mobile-carrier density, increasing electrical conductivity under the stated comparison.
The gain is electronic doping of the carbon framework, rather than a claim that potassium strengthens every C-C bond or simply acts as a separate wire through the sample. Intercalation also changes layer separation and scattering, so conductivity depends on both carrier population and mobility.